I've been given an old (10+ yrs) Moen shower control valve that I want to use (it does apparently have pressure balancing built-in), but don't know which side is hot and which is cold. Does Moen always have the same configuration, and, if so, which is which?

The water heater has nothing to do with it. You need a shower control valve that won't let the water pressure change when the toilet is flushed. Moen makes just such a valve called a pressure balancing valve. Moen L82683 Positemp Tub/Shower Valve. http://www.moen.com

www.moen.com/consumer-support

shut off water to shower, remove knob by popping cover off and removing screw, remove valve cover by just pulling straight out. there will be a retaining clip that holds cartridge in you will need to remove, Pull out old cartridge and replace with new.

probably have a kink on how water line feeding valve..if possible to cut drywall bhind tub valve and inspect pipe at bottom plate...moen faucets are equipped w/ anti scald device, pressure balanced (newer models) and this could cause cold water to overwhelm hot water...

no but you will get a cross conection problem

This is taken from the Moen manual. You can download it here:
http://www.moen.com/shared/pdf/instruction_sheets/ins162e.pdf
Balance Spool Maintenance
The precise and instantaneous pressure control illustrated has been
achieved through the balancing spool, which has been manufactured to
exacting tolerances.
During construction or valve installation, foreign material such as solder
flux, pipe cuttings sand, dirt or wood is unavoidably introduced into the
water system. Occasionally, however, rare, these foreign materials can
cause the balancing spool to become stuck temporarily between the
rough-in and trim-out operations. If this happens, it will be apparent at
the trim-out test, in that the valve will deliver only a small trickle of water
or it will deliver only hot or cold water. If this occurs, proceed as follows:
1. Make sure that both the hot and cold water service lines are ON. Also,
make sure that both screwdriver stop-check valves are open. The valve
WILL NOT OPERATE unless both supplies are ON.
2. If the valve still does not function properly, turn off both the hot and
cold supplies and remove the balancing spool, using a wide blade
screwdriver. The inner piston of the balancing spool should shake
back and forth freely. If this is not the case, jar the spool on either
end to remove the foreign material and free the spool. When the
spool is free, replace it; turn ON both water supplies and the valve
will function properly. If you are unable to free the inner piston,
replace the entire spool.

If you have hard water, you probably have lime built up in the head.
Take the shower head off and soak in vinigar or CLR, and re-assemble.

HTH,

Mike...

This is a common problem with this type of shower mixer valve. They are not very good at regulating with pressure change. Your options are somewhat limited to not flushing the toilet or using any other taps when in use, repalce the mixer valve for a modern ceramic unit or installing a 2 vane hot & cold shower pump.

Did this unit come with water stops built into the faucet body? Some of the newer faucets have stops built in and they need to be turned on. Also if you aren't going to plumb the hot in, you will need to cap it off but it should run without it unless it has some sort of balance in it. I don't think so though.

Replacing the cartridge should solve the problem, the balancing spool is stuck, replacing it will solve the problem. The valve should look like this http://www.moen.ca/shared/pdf/3170pt.pdf . I have unstuck the spools in the past, soaking it in white vinegar will help to remove build up.